How to Solve the Initial Condition Problem for Finding A_x and A_y Expressions?

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Homework Help Overview

The discussion revolves around finding expressions for A_x and A_y in the context of an initial condition problem related to motion described by trigonometric functions. Participants are exploring the integration of velocity and position functions, specifically in relation to the initial conditions provided.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing different methods for deriving the expressions for position and velocity, including the use of cosine and sine functions. There is confusion regarding the application of initial conditions and how they affect the determination of constants A_x and A_y.

Discussion Status

Some participants are attempting to clarify the process of using initial conditions, while others are exploring different methods for solving the problem. There is an acknowledgment that one method may be more complex than another, and some guidance has been offered regarding setting t=0 to simplify calculations.

Contextual Notes

Participants are grappling with the implications of initial conditions on their calculations, particularly how to substitute values without leading to contradictions in their derived expressions. There is a mention of specific values for x(0) and x'(0) that are relevant to the discussion.

nhrock3
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i can't see how they got X and Y expressions
V_x is the derivative of X(t) by t
'A' and phi are needed to be found
but when i don't know how to innpur the initial condition to find A_x and A_y
because when we integrate x' expression bot sides i get
x(t)-x(0)=[A_x*cos(wt+phi)]/w - [A_x*cos(0+phi)]/w
so i can't put 'b' instead of x(0) but it doesn't give me A_x parameter value
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hi nhrock3! :smile:

(pleeeeeeeeeeease don't post such wide pictures! :redface:)
nhrock3 said:
i can't see how they got X and Y expressions
V_x is the derivative of X(t) by t

(have an omega: ω :smile:)

the general solution can be written either as cos(ωt + φ), or as Acosωt + Bsinωt …

the book uses the second method to get the constants :wink:
 
i only used the first
how to do the second?
 
uhh? :confused: x(0) = A, x'(0) = ωB
 
why uhh? :)
 
ahh ok i understand
 
why i can't do it the first method
i want to solve it the irst way
 
you can solve it the first way, it's just more difficult …

put t = 0 and chug away :smile:​
 
i put t=0
and get that phi=0
what next?
 

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